Analysis of orientational dynamics of single fluorophore trajectories from three-angle polarization experiments

Abstract

An algorithm of single fluorophore orientation reconstruction based on a recently proposed method [J. T. Fourkas, Opt. Lett. 26, 211 (2001)] is studied, which converts three measured intensities {I(0),I(45),I(90)} to the dipole orientation {I(T),theta,phi}. Fluctuations in the detected signals {deltaI(0),deltaI(45),deltaI(90)} caused by the shot noise results in different profiles in deltatheta and deltaphi, causing the originally equivalent coordinates (X,Y,Z) to separate into in-plane (X,Y) and out-of-plane (Z) components. The overall fluctuation in deltatheta turns out to be higher than deltaphi, and thus noise has a greater effect on the Z component of the signal than on the X and Y components. Therefore, care should be taken not to interpret differences in the in-plane and out-of-plane dynamics as being evidence of nonisotropic rotational motion. For some molecular orientations around Theta=pi2, the total signal intensity cannot be inverted directly to angular coordinates. An optimization method is proposed that calculates the corrected angular coordinates for the points in the trajectory. To test the effects of this recovery scheme, the covariance/correlation functions for reconstructed angular trajectories were calculated for the case of isotropic rotational diffusion. Rotational correlation functions of rank [script-l] were found to deviate from the ideal single exponential decay as a result of the noise. This effect becomes more significant for large [script-l] cases. The correlation functions were fitted to a stretch exponential to characterize their deviation from the true single exponential decay. Correlation functions of Z have larger deviations from the true correlation function due to the larger noise in the Z component. The trends and the distributions of stretched exponential parameters {tau(F)} and {beta(F)} fitted from trajectories of a given size T also exhibit the influences from noise. Again, large [script-l] cases show a greater effect from the noise which eliminates the benefit of calculating higher rank correlation functions because of the smaller time constants. Due to the errors in estimating the correlation functions, significant differences between correlation functions of different orders can result from the statistics rather than being an indication of a nondiffusive behavior.

Angular measurements of the dynein ring reveal a stepping mechanism dependent on a flexible stalk

“…S2). The orientation of the probe emission dipole, parallel to the long axis of the QR (39), is determined from the relative intensities of the four component polarized fluorescence intensities in each image (42). Orientation is expressed in terms of angles α and β relative to the MT (Fig.…”

Fluorescence microscopy for simultaneous observation of 3D orientation and movement and its application to quantum rod-tagged myosin V

“…This result is because the function for δΦ has a sin 2 Θ factor in the denominator. Unlike δΦ, δΘ has an additional singular region at Θ ¼ 90°, because a sin 2Θ factor rather sin 2 Θ appears in the denominator (10).…”

Transient Three-Dimensional Orientation of Molecular Ions in an Ordered Polyelectrolyte Membrane

“…The factors A-C in the equations are NA dependent (see the SI). 14 There is 8-fold degeneracy for the experimental environment with respect to these trigonometric functions 15,18 ; angles explored by a dipole are mapped to 90° quadrants in the calculated polar and azimuthal angle planes. Detailed descriptions of the method, the analytical function space, and simulations are found in the SI.…”